Triangle calculator SSA

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Triangle has two solutions with side c=7.58112287925 and with side c=4.5788413467

#1 Obtuse scalene triangle.

Sides: a = 6.4   b = 2.5   c = 7.58112287925

Area: T = 7.57772239268
Perimeter: p = 16.48112287925
Semiperimeter: s = 8.24106143963

Angle ∠ A = α = 53.09897651335° = 53°5'23″ = 0.92765912007 rad
Angle ∠ B = β = 18.2° = 18°12' = 0.31876499239 rad
Angle ∠ C = γ = 108.7110234867° = 108°42'37″ = 1.8977351529 rad

Height: ha = 2.36878824771
Height: hb = 6.06217791415
Height: hc = 1.99989434785

Median: ma = 4.65500016132
Median: mb = 6.9033261186
Median: mc = 3.03991187043

Inradius: r = 0.91994974504
Circumradius: R = 4.00221141599

Vertex coordinates: A[7.58112287925; 0] B[0; 0] C[6.08798211298; 1.99989434785]
Centroid: CG[4.55436833074; 0.66663144928]
Coordinates of the circumscribed circle: U[3.79106143963; -1.28438069354]
Coordinates of the inscribed circle: I[5.74106143963; 0.91994974504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.9110234867° = 126°54'37″ = 0.92765912007 rad
∠ B' = β' = 161.8° = 161°48' = 0.31876499239 rad
∠ C' = γ' = 71.29897651335° = 71°17'23″ = 1.8977351529 rad




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6.4 ; ; b = 2.5 ; ; c = 7.58 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6.4+2.5+7.58 = 16.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.48 }{ 2 } = 8.24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.24 * (8.24-6.4)(8.24-2.5)(8.24-7.58) } ; ; T = sqrt{ 57.41 } = 7.58 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.58 }{ 6.4 } = 2.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.58 }{ 2.5 } = 6.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.58 }{ 7.58 } = 2 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.4**2-2.5**2-7.58**2 }{ 2 * 2.5 * 7.58 } ) = 53° 5'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-6.4**2-7.58**2 }{ 2 * 6.4 * 7.58 } ) = 18° 12' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.58**2-6.4**2-2.5**2 }{ 2 * 2.5 * 6.4 } ) = 108° 42'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.58 }{ 8.24 } = 0.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.4 }{ 2 * sin 53° 5'23" } = 4 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.4   b = 2.5   c = 4.5788413467

Area: T = 4.57659948708
Perimeter: p = 13.4788413467
Semiperimeter: s = 6.73992067335

Angle ∠ A = α = 126.9110234867° = 126°54'37″ = 2.21550014529 rad
Angle ∠ B = β = 18.2° = 18°12' = 0.31876499239 rad
Angle ∠ C = γ = 34.89897651335° = 34°53'23″ = 0.60989412768 rad

Height: ha = 1.43299983971
Height: hb = 3.66107958966
Height: hc = 1.99989434785

Median: ma = 1.83546484506
Median: mb = 5.42220323623
Median: mc = 4.28553859256

Inradius: r = 0.67990109061
Circumradius: R = 4.00221141599

Vertex coordinates: A[4.5788413467; 0] B[0; 0] C[6.08798211298; 1.99989434785]
Centroid: CG[3.55327448656; 0.66663144928]
Coordinates of the circumscribed circle: U[2.28992067335; 3.28327504139]
Coordinates of the inscribed circle: I[4.23992067335; 0.67990109061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 53.09897651335° = 53°5'23″ = 2.21550014529 rad
∠ B' = β' = 161.8° = 161°48' = 0.31876499239 rad
∠ C' = γ' = 145.1110234867° = 145°6'37″ = 0.60989412768 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.4 ; ; b = 2.5 ; ; beta = 18° 12' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 2.5**2 = 6.4**2 + c**2 -2 * 2.5 * c * cos (18° 12') ; ; ; ; c**2 -12.16c +34.71 =0 ; ; p=1; q=-12.1596422595; r=34.71 ; ; D = q**2 - 4pr = 12.16**2 - 4 * 1 * 34.71 = 9.0168998794 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 12.16 ± sqrt{ 9.02 } }{ 2 } ; ; c_{1,2} = 6.07982112976 ± 1.50140766278 ; ;
c_{1} = 7.58122879254 ; ; c_{2} = 4.57841346698 ; ; ; ; (c -7.58122879254) (c -4.57841346698) = 0 ; ; ; ; c>0 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6.4 ; ; b = 2.5 ; ; c = 4.58 ; ;

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6.4+2.5+4.58 = 13.48 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.48 }{ 2 } = 6.74 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.74 * (6.74-6.4)(6.74-2.5)(6.74-4.58) } ; ; T = sqrt{ 20.94 } = 4.58 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.58 }{ 6.4 } = 1.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.58 }{ 2.5 } = 3.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.58 }{ 4.58 } = 2 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.4**2-2.5**2-4.58**2 }{ 2 * 2.5 * 4.58 } ) = 126° 54'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-6.4**2-4.58**2 }{ 2 * 6.4 * 4.58 } ) = 18° 12' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.58**2-6.4**2-2.5**2 }{ 2 * 2.5 * 6.4 } ) = 34° 53'23" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.58 }{ 6.74 } = 0.68 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.4 }{ 2 * sin 126° 54'37" } = 4 ; ;




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